Basic Examples (4) 

Combine the powers in an expression:

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Combine powers with multiple terms:

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Combine radicals:

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DisplayPowersTogether also combines products and quotients that include CubeRoot:

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Scope (9) 

DisplayPowersTogether combines exponents using the default assumptions stored in $Assumptions. The assumptions in this example are sufficient to combine all the exponents:

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DisplayPowersTogether similarly combines all the exponents when is given as a second argument in DisplayPowersTogether:

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Provide assumptions allowing some but not all exponents to be combined:

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Set $Assumptions as a>0, and specify d>0 as an assumption within DisplayPowersTogether:

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Only assume d > 0:

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The following assumptions are sufficient to combine all the exponents even though nothing is assumed about b or z:

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FullSimplify verifies that DisplayPowersTogether performed a valid transformation under the given assumptions:

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This performs independent verification by searching for a counterexample to the previous example. The identity is True in every case considered:

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In this case, nothing is assumed and none of the exponents can be combined:

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DisplayPowersTogether determines this can be done with a single Sqrt:

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Surd is a generalization of CubeRoot. DisplayPowersTogether combines expressions involving Surd when appropriate:

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Properties and Relations (2) 

Rather than use $Assumptions or DisplayPowersTogether[expr,assum], assumptions can be provided using Assuming:

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Two examples are given here where Simplify can combine a sum of terms:

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DisplayPowersTogether does not handle sums or differences:

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Possible Issues (2) 

The result of DisplayPowersTogether has a Head of Defer:

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It is not a readily-computable expression:

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First can be used to compute on the results:

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Alternatively, copy the output shown previously and evaluate it to perform the computation:

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DisplayPowersTogether can be used again to ensure the square roots are combined again:

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The next example is not in a form that allows DisplayPowersTogether to combine factors:

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When the cube root above is distributed across the sum, DisplayPowersTogether can combine factors:

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